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Question #43510
The Question
A solid uniform sphere of mass and radius is placed on the rough horizontal bed of a truck. The truck accelerates to the right with a constant acceleration . A horizontal force of magnitude is applied to the topmost point of the sphere, also directed to the right. Assuming the sphere rolls without slipping on the truck bed, what is the magnitude and direction of the static friction force acting on the sphere?
Options
- A.
towards the right
- B.
towards the right
- C.
towards the right
- D.
towards the left
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Variable_Constraint
Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.
Concepts Behind This Question
Pure Rolling Condition|Pseudo Force Directionality|Non-Uniform Acceleration Constraint
Why This Question Is Tricky
Common Mistakes
The core trap lies in the misapplication of torque and rolling constraints in a non-inertial reference frame.
Students frequently attempt to solve this by taking torque about the contact point in the truck's frame but forget to include the torque produced by the pseudo force acting at the center of mass.
Alternatively, if solved in the ground frame, students often incorrectly assume the acceleration of the contact point is zero () instead of matching the truck's acceleration ().
Both of these 'inertial assumption' errors lead directly to the incorrect friction value of .
This problem rigorously tests the synthesis of non-inertial dynamics with kinematic rolling constraints.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | System of Particles and Rotational Motion - Class 11 Part 1 |
| Concept | Pure Rolling Condition |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |